Update README.md

Author: leclere

README.md

@@ -9,32 +9,40 @@
 [![codecov.io](https://codecov.io/github/leclere/StochDynamicProgramming.jl/coverage.svg?branch=master)](https://codecov.io/github/leclere/StochDynamicProgramming.jl?branch=master)
 
 
-This is a Julia implementation of the *Stochastic Dual Dynamic Programming* (SDDP) algorithm. It is built upon [JuMP](https://github.com/JuliaOpt/JuMP.jl)
+This is a Julia package for optimizing controlled stochastic dynamic system (in discrete time). It offers three methods of resolution :
 
+- Extensive formulation
+- Stochastic Dynamic Programming.
+- *Stochastic Dual Dynamic Programming* (SDDP) algorithm. 
 
-## Why SDDP?
-
-SDDP is an algorithm to solve multistage stochastic optimization problems.
-It return bounds on the value of the optimization problem and approximation
-of Bellman function that are used to derive an optimal solution.
+It is built upon [JuMP](https://github.com/JuliaOpt/JuMP.jl)
 
-These problems are modelled with:
+## What problem can we solve with this package ?
 
-- stage-wise independent discrete noise
+- Stage-wise independent discrete noise
+- Linear dynamics
+- Linear or convex piecewise linear cost
+Extension to non-linear formulation are under development.
 
-- Linear dynamic
+## Why Extensive formulation ?
 
-- Linear or piecewise linear cost
+An extensive formulation approach consists in representing the problem in a linear
+problem solved by an external linear solver. Complexity is exponential in number of stages. 
 
+## Why Stochastic Dynamic Programming ?
 
-This algorithm could be applied to the following examples:
+Dynamic Programming is a standard tool to solve stochastic optimal control problem with
+independent noise. The method require discretisation of the state space, and is exponential
+in the dimension of the state space.
 
-- Dams valley management
-
-- Newsvendor testcase
+## Why SDDP?
 
+SDDP is a dynamic programming algorithm relying on cutting planes. The algorithm require convexity
+of the value function but does not discretize the state space. The complexity is linear in the
+number of stage, and can accomodate higher dimension state than standard dynamic programming. 
+The algorithm return exact lower bound and estimated upper bound as well as approximate optimal
+control strategies.
 
-The documentation will be soon updated to explain how this algorithm work.
 
 
 ## Installation